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Mathematical Expression Editor
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Notation and Geometric Ideas
Identify the type of integral described by the notation.
An integral of the
form is a:
What does this integral represent geometrically?
Does the orientation of matter for the integral?
An integral of the form is a:
What does this integral represent geometrically?
If for some constant , then is:
The integral will be negative in which of the following instances (select all):
An integral of the form is a:
What does this integral represent geometrically?
If , then is:
Does orientation of matter for this type of integral?
An integral of the form is a:
Computations
These questions are more open ended but are meant to guide your studying a
bit.
What is your thought process when asked to evaluate for some and
some ?
What is your thought process when asked to evaluate for some and some
?
What is your thought process when asked to evaluate for some vector field
and some ?
How do you check whether a vector field is conservative? How does this
relate to the curl?
What does the Fundamental Theorem of Line Integrals say, and what are its
main consequences for the purposes of this class?
How can the Fundamental Theorem of Line Integrals and its consequences
help you compute vector line integrals?
When can you use the Fundamental Theorem of Line Integrals?
What does Green’s Theorem say? What are its conditions, and in what
instances can it be used?
Can we use Green’s Theorem if is conservative? What does it tell us in this
case?
Suppose we have a line integral . If we need to close the curve to use
Green’s Theorem, what are the steps we must carry out in order to solve the
original integral?
When given a vector line integral , what is your thought process in
determining what method to use?
Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)
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Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)